There are many websites that specialise in the trading industry; Cityjobs and Junior Broker are both fairly good. The other thing to consider is an internship, I have seen this a lot in the city, it would obviously be unpaid initially but there is potential for a permanent job to arise as a result of completing an internship successfully and professionally.
Maybe also consider friends and family, do you have a friend whose father works in the industry, or even a friend of a friend. Linkedin is good for networking, you can also search for jobs by industry, then try connecting with people that are in a field of work that interests you, I regularly get requests from people I have never heard of, it’s worth accepting them and also making the requests yourself, you never know who you may end up connecting with, your future boss…….?